Niveau: Supérieur, Doctorat, Bac+8
KAHLER MANIFOLDS WITH NUMERICALLY EFFECTIVE RICCI CLASS Jean-Pierre Demailly?, Thomas Peternell??, Michael Schneider?? ? Universite de Grenoble I ?? Universitat Bayreuth Institut Fourier, BP 74 Mathematisches Institut U.R.A. 188 du C.N.R.S. Postfach 10 12 51 38402 Saint-Martin d'Heres, France D-8580 Bayreuth, Deutschland Introduction Compact Kahler manifolds with semipositive Ricci curvature have been investigated by various authors. S. Kobayashi [Ko61] first proved the simple connectedness of Fano manifolds, namely manifolds with positive Ricci curvature or equivalently, with ample anticanonical line bundle ?KX . Later on, generalizing results of Y. Matsushima [Ma69], A. Lichnerowicz [Li71, 72] proved the following interesting fibration theorem: if X is a compact Kahler manifold with semipositive Ricci class, then X is a smooth fibration over its Albanese torus and there is a group of analytic automorphisms of X lying over the group of torus translations (see also Section 2 for another proof of these facts based on the solution of Calabi's conjecture and on Bochner's technique). Finally, there were extensive works in the last decades to study the structure and classification of Ricci flat Kahler manifolds, see e.g. [Ca57], [Bo74a,b], [Be83] and [Kr86] ; of special interest for physicists is the subclass of so-called Calabi-Yau manifolds, i.
- subexponential growth cannot
- line bundle
- geometric technique
- group has polynomial
- known differential
- compact kahler
- ricci
- ricci flat compact
- gromov's well-known